There is no guarantee that it is 1:1. I can send Bitcoin to a mint to create ecash, then withdrawal the Bitcoin from that wallet without effecting the amount of ecash. Then it is backed 0:1. You can still send the ecash to someone, but if anyone tries to redeem ecash for sats, it will fail.
Discussion
It’s not perfect rn it’s a brand new layer 3 . If you did what you said your ecash would be unspendable until there were sats in the mint. For now I would not accept payment in ecash directly I would post a regular lightning invoice and the payer can use ecash to pay the lightning invoice.
Prove you can do that, in a screen grab. Entanglement is primary to fedimints and chaum. You are saying they've been working on this for years only to un invent bitcoin scarcity.
I'm Not saying it's impossible, it sort of is re-inventing a fiat like middleman, what i am saying is there are many eyes on this and i would appreciate proof.
Show yourself redeeming tokens sent to your mint but intended for someone else.